IJPAM: Volume 97, No. 4 (2014)

RADIO NUMBER FOR CROSS PRODUCT $P_n(P_2)$

Chahn Yong Jung$^1$, Waqas Nazeer$^2$, Saima Nazeer$^3$,
Arif Rafiq$^4$ and Shin Min Kang$^5$
$^1$Department of Business Administration
Gyeongsang National University
Jinju, 660-701, KOREA
$^{2,4}$Department of Mathematics
Lahore Leads University
Lahore, 54810, PAKISTAN
$^3$Department of Mathematics
Lahore College for Women University
Lahore, 54600, PAKISTAN
$^5$Department of Mathematics and RINS
Gyeongsang National University
Jinju, 660-701, KOREA


Abstract. A Radio labeling of the graph $G$ is a function $g$ from the vertex set $V(G)$ of $G$ to $\mathbb{N}\cup\{0\}$ such that $\vert f(u)-f(v)\vert\geq diam(G)+1-d_G(u,v)$, where $diam(G)$ and $d_G(u,v)$ are diameter and distance between $u$ and $v$ in graph $G,$ respectively. The radio number $rn(G)$ of $G$ is the smallest number $k$ such that $G$ has radio labeling with $\max\{f(v):v\in V(G)\}=k$. We investigate radio number for the cross product of $P_n$ and $P_2$.

Received: August 28, 2014

AMS Subject Classification: 05C12, 05C15, 05C78

Key Words and Phrases: channel assignment, radio labeling, radio number, cross product

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DOI: 10.12732/ijpam.v97i4.11 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 97
Issue: 4
Pages: 515 - 525


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